This invention relates generally to ultrasonic flow rate measurement, and more particularly to multi-path ultrasonic flow meter.
Ultrasonic flow meters are used to determine the flow rate (i.e., mean pipe flow rate (Vm)) of a variety of fluids (e.g., liquids, gases, etc.) and speed of sound in the fluid flowing in pipes of different sizes and shapes. Knowledge of the flow rate of the fluid can enable other physical properties or qualities of the fluid to be determined. For example, in some custody-transfer applications, the flow rate can be used to determine the volume (Q) of a fluid (e.g., oil or gas) being transferred from a seller to a buyer through a pipe to determine the costs for the transaction, where the volume is equal to the flow rate multiplied by the cross sectional area (A) of the pipe. In other applications, the speed of sound can be used to determine the mean molecular weight of a fluid flowing in a pipe to optimize and control chemical or combustion processes.
In one type of ultrasonic flow meter employing transit time flow metering, one or more pairs of ultrasonic transducers can be attached to a pipe (or spool piece attached to a pipeline), where each pair can contain transducers located upstream and downstream from each other forming an ultrasonic path between them. Each transducer, when energized, transmits an ultrasonic signal (e.g., a sound wave) along an ultrasonic path through the flowing fluid that is received by and detected by the other transducer. The path velocity (i.e., path or chord velocity (Vp)) of the fluid averaged along an ultrasonic path can be determined as a function of the differential between (i) the transit time of an ultrasonic signal traveling along the ultrasonic path from the downstream transducer upstream to the upstream transducer against the fluid flow direction, and (2) the transit time of an ultrasonic signal traveling along the ultrasonic path from the upstream transducer downstream to the downstream transducer with the fluid flow direction.
The path velocity (Vp) of the fluid averaged along one or more ultrasonic paths between the pairs of transducers does not necessarily represent the flow rate (Vm) of the fluid across the entire cross section of the pipe since path velocity has a radial distribution wherein the flow velocity across the pipe is not necessarily uniform (i.e., all of the fluid in the pipe does not flow at the same path velocity). This radial distribution of the flow velocity is described by its flow profile (or fluid velocity profile), which is a function of several factors, including the Reynolds number (Re). The Reynolds number (Re) is a dimensionless number that characterizes the behavior of fluids flowing through a pipe by providing a measure of the ratio of the inertial force (i.e., flow rate (Vm)) to the viscous force (i.e., kinematic viscosity (v)) of the fluid flowing in a closed circular pipe with a known diameter (D), and is equal to the product of the flow rate and the pipe diameter divided by the kinematic viscosity of the fluid (Re=(Vm*D)/v). Knowledge of the Reynolds number allows for the determination of the profile of fluid flow in the pipe: (1) for a relatively low Reynolds number (e.g., Re<2300), laminar profile (parabolic shape where the maximum path velocity is at the center of the pipe and the flow velocity gradually decreases to zero at the pipe wall); (2) for a relatively high Reynolds number (e.g., Re>4000), turbulent profile (flattened shape where the flow velocity is virtually constant except for an area near the pipe wall); and (3) for an intermediate Reynolds number (e.g., 2300<Re<4000), transitional profile (combination of laminar and turbulent).
In addition to the Reynolds number, which is generally the principal factor affecting a flow profile and is dependent on the kinematic viscosity of the fluid, the flow profile is also a function of several other factors, including fluid characteristics, pipe roughness, pipe configuration (e.g., straight, bends, elbows, tees, valves, headers, etc.), and disturbances caused by the transducer ports. Accordingly, in order to determine the flow profile for a particular ultrasonic flow meter installation, a number of installation-specific pieces of information would be required, including knowledge of several of the physical properties of the fluid and the pipe, some of which may change over time (e.g., relative pipe wall roughness (ε/D)).
Rather than determining a flow profile, prior art solutions using multiple paths (Pi) and multiple path velocities (Vpi), select the locations of the transducer pairs (i.e., the ultrasonic paths) and the weights (wi) to be assigned to each path velocity (Vpi) in determining a mean flow rate (Vm) based on one or more known mathematical techniques (e.g., Gaussian Quadrature, Chebycheff, Lobatto, etc.) as described in, for example, U.S. Pat. Nos. 3,564,950 and 3,940,985.
While these prior art solutions minimize the need to determine some installation-specific pieces of information required to determine the flow profile, the solutions only provide moderate to high accuracy for a flow profile that requires a high order polynomial required to describe it (i.e., the higher the complexity of the flow profile, the higher the order of the polynomial) unless there are sufficient ultrasonic paths and transducers provided in the ultrasonic flow meter to improve the accuracy. For example, if a 15th order polynomial is required to describe the flow profile, a total of eight ((15+1)/2) ultrasonic paths and transducer pairs can be required for improved accuracy, which would also increase the cost of the flow meter, increase the difficulty of installation of large number of transducers given the space constraints on a pipe, and increase the disturbances to the flow causes by the large number of transducer ports. Furthermore, since several ultrasonic flow meter applications require highly accurate flow rate (Vm) measurements (e.g., custody-transfer applications for liquid hydrocarbons often require an accuracy of 0.15%) that cannot always be achieved by simply increasing the number of ultrasonic paths and transducers in these prior art solutions, complicated calibration schemes using calibration factors that are based on several of the physical properties of the fluid and/or the pipe (e.g., the Reynolds number) are required anyway to achieve the required accuracy, which increases the costs and complexity of the flow meters.
It would be advantageous to provide an ultrasonic flow meter that can provide highly accurate flow rate measurements without the use of complicated flow meter design and calibration schemes.